arXiv subjects

Kangjie Zhou

Publications and source records attributed to Kangjie Zhou.

26 records · Page 2Linked to original sources

arXiv2024

SwarmPRM: Probabilistic Roadmap Motion Planning for Large-Scale Swarm Robotic Systems

Large-scale swarm robotic systems consisting of numerous cooperative agents show considerable promise for performing autonomous tasks across various sectors. Nonetheless, traditional motion planning approaches often face a trade-off between scalability and solution quality due to the exponential growth of the joint state space of robots. In response, this work proposes SwarmPRM, a hierarchical, scalable, computationally efficient, and risk-aware sampling-based motion planning approach for large-scale swarm robots. SwarmPRM utilizes a Gaussian Mixture Model (GMM) to represent the swarm's macroscopic state and constructs a Probabilistic Roadmap in Gaussian space, referred to as the Gaussian roadmap, to generate a transport trajectory of GMM. This trajectory is then followed by each robot at the microscopic stage. To enhance trajectory safety, SwarmPRM incorporates the conditional value-at-risk (CVaR) in the collision checking process to impart the property of risk awareness to the constructed Gaussian roadmap. SwarmPRM then crafts a linear programming formulation to compute the optimal GMM transport trajectory within this roadmap. Extensive simulations demonstrate that SwarmPRM outperforms state-of-the-art methods in computational efficiency, scalability, and trajectory quality while offering the capability to adjust the risk tolerance of generated trajectories.

cs.RO↗

arXiv2024

Probabilistic Visibility-Aware Trajectory Planning for Target Tracking in Cluttered Environments

Target tracking has numerous significant civilian and military applications, and maintaining the visibility of the target plays a vital role in ensuring the success of the tracking task. Existing visibility-aware planners primarily focus on keeping the target within the limited field of view of an onboard sensor and avoiding obstacle occlusion. However, the negative impact of system uncertainty is often neglected, rendering the planners delicate to uncertainties in practice. To bridge the gap, this work proposes a real-time, non-myopic trajectory planner for visibility-aware and safe target tracking in the presence of system uncertainty. For more accurate target motion prediction, we introduce the concept of belief-space probability of detection (BPOD) to measure the predictive visibility of the target under stochastic robot and target states. An Extended Kalman Filter variant incorporating BPOD is developed to predict target belief state under uncertain visibility within the planning horizon. To reach real-time trajectory planning, we propose a computationally efficient algorithm to uniformly calculate both BPOD and the chance-constrained collision risk by utilizing linearized signed distance function (SDF), and then design a two-stage strategy for lightweight calculation of SDF in sequential convex programming. Extensive simulation results with benchmark comparisons show the capacity of the proposed approach to robustly maintain the visibility of the target under high system uncertainty. The practicality of the proposed trajectory planner is validated by real-world experiments.

cs.RO↗

arXiv2024

CAMON: Cooperative Agents for Multi-Object Navigation with LLM-based Conversations

Visual navigation tasks are critical for household service robots. As these tasks become increasingly complex, effective communication and collaboration among multiple robots become imperative to ensure successful completion. In recent years, large language models (LLMs) have exhibited remarkable comprehension and planning abilities in the context of embodied agents. However, their application in household scenarios, specifically in the use of multiple agents collaborating to complete complex navigation tasks through communication, remains unexplored. Therefore, this paper proposes a framework for decentralized multi-agent navigation, leveraging LLM-enabled communication and collaboration. By designing the communication-triggered dynamic leadership organization structure, we achieve faster team consensus with fewer communication instances, leading to better navigation effectiveness and collaborative exploration efficiency. With the proposed novel communication scheme, our framework promises to be conflict-free and robust in multi-object navigation tasks, even when there is a surge in team size.

cs.RO↗

arXiv2024

ASPIRe: An Informative Trajectory Planner with Mutual Information Approximation for Target Search and Tracking

This paper proposes an informative trajectory planning approach, namely, \textit{adaptive particle filter tree with sigma point-based mutual information reward approximation} (ASPIRe), for mobile target search and tracking (SAT) in cluttered environments with limited sensing field of view. We develop a novel sigma point-based approximation to accurately estimate mutual information (MI) for general, non-Gaussian distributions utilizing particle representation of the belief state, while simultaneously maintaining high computational efficiency. Building upon the MI approximation, we develop the Adaptive Particle Filter Tree (APFT) approach with MI as the reward, which features belief state tree nodes for informative trajectory planning in continuous state and measurement spaces. An adaptive criterion is proposed in APFT to adjust the planning horizon based on the expected information gain. Simulations and physical experiments demonstrate that ASPIRe achieves real-time computation and outperforms benchmark methods in terms of both search efficiency and estimation accuracy.

cs.RO↗

arXiv2023

Informative Path Planning of Autonomous Vehicle for Parking Occupancy Estimation

Parking occupancy estimation holds significant potential in facilitating parking resource management and mitigating traffic congestion. Existing approaches employ robotic systems to detect the occupancy status of individual parking spaces and primarily focus on enhancing detection accuracy through perception pipelines. However, these methods often overlook the crucial aspect of robot path planning, which can hinder the accurate estimation of the entire parking area. In light of these limitations, we introduce the problem of informative path planning for parking occupancy estimation using autonomous vehicles and formulate it as a Partially Observable Markov Decision Process (POMDP) task. Then, we develop an occupancy state transition model and introduce a Bayes filter to estimate occupancy based on noisy sensor measurements. Subsequently, we propose the Monte Carlo Bayes Filter Tree, a computationally efficient algorithm that leverages progressive widening to generate informative paths. We demonstrate that the proposed approach outperforms the benchmark methods in diverse simulation environments, effectively striking a balance between optimality and computational efficiency.

cs.RO↗

arXiv2023

Tractability from overparametrization: The example of the negative perceptron

In the negative perceptron problem we are given $n$ data points $({\boldsymbol x}_i,y_i)$, where ${\boldsymbol x}_i$ is a $d$-dimensional vector and $y_i\in\{+1,-1\}$ is a binary label. The data are not linearly separable and hence we content ourselves to find a linear classifier with the largest possible \emph{negative} margin. In other words, we want to find a unit norm vector ${\boldsymbol θ}$ that maximizes $\min_{i\le n}y_i\langle {\boldsymbol θ},{\boldsymbol x}_i\rangle$. This is a non-convex optimization problem (it is equivalent to finding a maximum norm vector in a polytope), and we study its typical properties under two random models for the data. We consider the proportional asymptotics in which $n,d\to \infty$ with $n/d\toδ$, and prove upper and lower bounds on the maximum margin $κ_{\text{s}}(δ)$ or -- equivalently -- on its inverse function $δ_{\text{s}}(κ)$. In other words, $δ_{\text{s}}(κ)$ is the overparametrization threshold: for $n/d\le δ_{\text{s}}(κ)-\varepsilon$ a classifier achieving vanishing training error exists with high probability, while for $n/d\ge δ_{\text{s}}(κ)+\varepsilon$ it does not. Our bounds on $δ_{\text{s}}(κ)$ match to the leading order as $κ\to -\infty$. We then analyze a linear programming algorithm to find a solution, and characterize the corresponding threshold $δ_{\text{lin}}(κ)$. We observe a gap between the interpolation threshold $δ_{\text{s}}(κ)$ and the linear programming threshold $δ_{\text{lin}}(κ)$, raising the question of the behavior of other algorithms.

cs.LG↗

arXiv2021

Variance Reduction for Causal Inference

Propensity score methods have been shown to be powerful in obtaining efficient estimators of average treatment effect (ATE) from observational data, especially under the existence of confounding factors. When estimating, deciding which type of covariates need to be included in the propensity score function is important, since incorporating some unnecessary covariates may amplify both bias and variance of estimators of ATE. In this paper, we show that including additional instrumental variables that satisfy the exclusion restriction for outcome will do harm to the statistical efficiency. Also, we prove that, controlling for covariates that appear as outcome predictors, i.e. predict the outcomes and are irrelevant to the exposures, can help reduce the asymptotic variance of ATE estimation. We also note that, efficiently estimating the ATE by non-parametric or semi-parametric methods require the estimated propensity score function, as described in Hirano et al. (2003)\cite{Hirano2003}. Such estimation procedure usually asks for many regularity conditions, Rothe (2016)\cite{Rothe2016} also illustrated this point and proposed a known propensity score (KPS) estimator that requires mild regularity conditions and is still fully efficient. In addition, we introduce a linearly modified (LM) estimator that is nearly efficient in most general settings and need not estimation of the propensity score function, hence convenient to calculate. The construction of this estimator borrows idea from the interaction estimator of Lin (2013)\cite{Lin2013}, in which regression adjustment with interaction terms are applied to deal with data arising from a completely randomized experiment. As its name suggests, the LM estimator can be viewed as a linear modification on the IPW estimator using known propensity scores. We will also investigate its statistical properties both analytically and numerically.

stat.ME↗

arXiv2021

Propensity Score Adapted Covariate Selection for Causal Inference

In this paper, we propose a propensity score adapted variable selection procedure to select covariates for inclusion in propensity score models, in order to eliminate confounding bias and improve statistical efficiency in observational studies. Our variable selection approach is specially designed for causal inference, it only requires the propensity scores to be $\sqrt{n}$-consistently estimated through a parametric model and need not correct specification of potential outcome models. By using estimated propensity scores as inverse probability treatment weights in performing an adaptive lasso on the outcome, it successfully excludes instrumental variables, and includes confounders and outcome predictors. We show its oracle properties under the "linear association" conditions. We also perform some numerical simulations to illustrate our propensity score adapted covariate selection procedure and evaluate its performance under model misspecification. Comparison to other covariate selection methods is made using artificial data as well, through which we find that it is more powerful in excluding instrumental variables and spurious covariates.

stat.ME↗